Question

plz explain factor theorem ??

Answer 1

If p(x) is a polynomial of degree n > 1 and a is any real number, then

x – a is a factor of p(x), if p(a) = 0, and

p(a) = 0, if x – a is a factor of p(x).

Let’s look at an example to understand this theorem better.

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Maths > Polynomials > Factor Theorem

Polynomials

Factor Theorem

In this part, we will look at the Factor Theorem, which uses the remainder theorem and learn how to factorise polynomials. Further, we will be covering the splitting method and the factor theorem method.

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Factor Theorem

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If p(x) is a polynomial of degree n > 1 and a is any real number, then

x – a is a factor of p(x), if p(a) = 0, and

p(a) = 0, if x – a is a factor of p(x).

Let’s look at an example to understand this theorem better.

Browse more Topics under Polynomials

Polynomial and its Types

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Factorisation of Polynomials

Remainder Theorem

Zeroes of Polynomial

Geometrical Representation of Zeroes of a Polynomial

Example:

Examine whether x + 2 is a factor of x3 + 3x2 + 5x + 6

Solution: To begin with, we know that the zero of the polynomial (x + 2) is –2. Let p(x) = x3 + 3x2 + 5x + 6

Then, p(–2) = (–2)3 + 3(–2)2 + 5(–2) + 6 = –8 + 12 – 10 + 6 = 0

According to the factor theorem, if p(a) = 0, then (x – a) is a factor of p(x). In this example, p(a) = p(- 2) = 0

Therefore, (x – a) = {x – (-2)} = (x + 2) is a factor of ‘x3 + 3x2 + 5x + 6’ or p(x).

hope it helps

Answer 2

$\huge\underline\mathscr\red{Answer:-}$

In algebra,Factor Theorem is a theorem linking factors of zeroes of a polynomial.

It is a special case of the polynomial remainder theorem.

The factor theorem states that a polynomial:-

f(x) has a factor (x-k) if and only if

f(k)=0(i.e., k is a root).

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HOPE IT HELPS UHH DEAR❤